Tidal dissipation within large icy satellites: Applications to Europa and Titan

This paper describes a new approach based on variational principles to calculate the radial distribution of tidal energy dissipation in any satellite. The advantage of the model with respect to classical solutions, is that it relates in a straightforward way the radial distribution of the time-averaged dissipation rate to its sensitivity to the corresponding distribution of viscoelastic parameters. This method is applied to Io-, Europa-, and Titan-like interiors, and it is tested against the results obtained by two classical methods by determining global dissipation as well as radial and lateral distributions within satellite interiors. By exploring systematically the different parameters defining the interior models, we demonstrate that the presence of a deep ocean below an outer ice layer strongly influences the tidal dissipation distribution in both the outer ice layer and in the innermost part of the satellite. On the one hand, the ocean by imposing a large radial displacement at the base of the outer ice I layer, controls the distribution of tidal strain rate within the outer layer, making the tidal strain rate field very weakly sensitive to the viscosity variations. Conversely, in the high-pressure ice layer below the ocean, both tidal strain rate and dissipation are very sensitive to any variation of the ice viscosity. On the other hand, for identical structures of the mantle and of the core, the presence of a subsurface ocean reduces the strength of dissipation in the silicate mantle. The existence of a liquid layer within Europa makes models of the silicate mantle less dissipative than the predictions for Io.